Finite Group Databasebeta

← #11857956

Subgroups — #11857956

Order 1152.

1625 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3#10594602C211yesmaximal, characteristic, complemented
4#10592470C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6C3×#4770C211yesmaximal, characteristic, complemented
7#10591421C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9#10591418C211yesmaximal, characteristic, complemented
10#10590957C211yesmaximal, characteristic, complemented
11#10590954C211yesmaximal, characteristic, complemented
12#10590948C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590608C211yesmaximal, characteristic, complemented
15#10590600C211yesmaximal, characteristic, complemented
16#78924—31nomaximal
17#78830—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237C418yescomplemented
27C2×C4×D32C2211yescharacteristic
28C2×#3796C2211yescharacteristic
29C2×#3795C2211yescharacteristic
30C2×D3×Dic6C2211yescharacteristic
31C2×#3743C2211yescharacteristic, complemented
32C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic, complemented
35C3×#892C2211yescharacteristic
36C3×#892C2211yescharacteristic, complemented
37#63921—21no—
38#63900C2211yescharacteristic, complemented
39C4×#624—21no—
40#63877—21no—
41#63877—21no—
42#63841C2211yescharacteristic
43#63841C2211yescharacteristic, complemented
44C2×#3712C2211yescharacteristic, complemented
45C2×#3711C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic, complemented
47D3×ΓL(1,𝔽25)—24no—
48C32×#102C2211yescharacteristic, complemented
49#63659C2211yescharacteristic, complemented
50#63643C2211yescharacteristic, complemented
51#63637C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64C2×D3×#41—31no—
65C22×#237—31no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68D3×#117—31no—
69D3×#117—31no—
70C3×#418—31no—
71C3×#416—31no—
72#5233—31no—
73#5215—31no—
74#5120—31no—
75#5113—31no—
76#5004—31no—
77#5002—31no—
78#4803—31no—
79#4803—31no—
80#4802—31no—
81#4802—31no—
82#4772—31no—
83#4772—31no—
84#4772—31no—
85#4772D311yescharacteristic, complemented
86#4771—31no—
87#4771—31no—
88#4771—31no—
89#4771—31no—
90#4771—31no—
91#4771—31no—
92#4771—61no—
93#4770—31no—
94#4770D311yescharacteristic, complemented
95C23×C3×D3—21no—
96C22×D32D411yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100#3830—22no—
101#3830C2×C414yes—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C3×#237—22no—
109C3×#237C2×C414yescomplemented
110C3×D3×D4—22no—
111C3×D3×D4C2×C414yescomplemented
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116D3×#67—28no—
117C2×#627—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#624—21no—
121C2×#624D411yescharacteristic
122#3805—28no—
123#3804—28no—
124C2×D3×Dic3—21no—
125C2×D3×Dic3—21no—
126C2×D3×Dic3—21no—
127C2×D3×Dic3—28no—
128C2×D3×Dic3D411yescharacteristic
129C2×D3×Dic3D411yescharacteristic
130C4×D32C2×C414yes—
131C4×D32D414yes—
132#3796—22no—
133#3796C2×C414yes—
134#3795—22no—
135#3795C2×C414yescomplemented
136D3×Dic6—22no—
137D3×Dic6C2×C414yescomplemented
138C2×C32×C8C2311yescharacteristic
139C32×C4⋊C4C2311yescharacteristic
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141#3750—21no—
142C2×C3⋊(C3⋊C8)C2311yescharacteristic
143#3743—22no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×C4×Dic3—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×ΓL(1,𝔽25)—22no—
153C3×D3×C8—22no—
154#3724—21no—
155(C2×D3)⋊Dic3—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3712—22no—
160#3711—22no—
161D3×C3⋊C8—22no—
162#2896—91noSylow
163C2×C3×#41—31no—
164C22×C3×D4—31no—
165C22×#67—61no—
166C23×Dic3—61no—
167D3×#41—38no—
168D3×#41—64no—
169C2×#239—31no—
170C2×D3×Q8—31no—
171C2×#237—31no—
172C2×#237—31no—
173C2×#237—38no—
174C2×#237—31no—
175C2×#237—31no—
176C2×#237—61no—
177C2×#237—64no—
178C2×#237—61no—
179C2×#237—61no—
180C2×#237—61no—
181C2×#237C2×D311yescharacteristic
182C2×D3×D4—61no—
183C2×D3×D4C2×D311yescharacteristic
184C2×#235—31no—
185C2×#235—61no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—61no—
189C22×Dic6—31no—
190C2×C3×M16—31no—
191C22×C3×C8—31no—
192C3×#117—31no—
193C3×#117—31no—
194#926—31no—
195#926—31no—
196C2×#208—31no—
197C22×C3⋊C8—31no—
198D3×M16—64no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—61no—
205C2×ΓL(1,𝔽25)—64no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207C2×D3×C8—31no—
208C2×D3×C8C2×D311yescharacteristic, complemented
209#892—31no—
210#892—31no—
211#892C2×D311yescharacteristic
212#892C2×D311yescharacteristic, complemented
213D3×C4⋊C4—31no—
214D3×C4⋊C4—31no—
215D3×C4⋊C4—31no—
216D3×C4⋊C4—31no—
217D3×C4⋊C4—61no—
218D3×C22⋊C4—61no—
219D3×C22⋊C4—61no—
220#877—61no—
221#877—61no—
222#872—61no—
223#872—61no—
224C42×D3—61no—
225C42×D3—61no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#102—21no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235#835—31no—
236#835—31no—
237#832—31no—
238#832—31no—
239#832—31no—
240#832—31no—
241#832—61no—
242#832C2×D311yescharacteristic, complemented
243#832C2×D311yescharacteristic, complemented
244#821—31no—
245#821C2×D311yescharacteristic, complemented
246#816—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—61no—
252#816C2×D311yescharacteristic, complemented
253#810—31no—
254#810—31no—
255#810—31no—
256#810—31no—
257#810—31no—
258#810—61no—
259#810C2×D311yescharacteristic, complemented
260#809—31no—
261#809C2×D311yescharacteristic, complemented
262C23×C32—21no—
263C22×C3⋊D3C2×D411yescharacteristic
264C22×C3×D3—21no—
265C22×C3×D3—24no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3C2×D411yescharacteristic
269C22×C3×D3C2×D411yescharacteristic
270C2×D32—41no—
271C2×D32—41no—
272C2×D32C22⋊C414yes—
273C32×D4—21no—
274C32×D4C22×C412yes—
275C2×C32×C4—21no—
276C2×C32×C4C2411yescharacteristic
277#638—24no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—24no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3C2×D411yescharacteristic
282C4×C3⋊D3—42no—
283C4×C3⋊D3C22×C412yes—
284C4×C3⋊D3C2×D412yes—
285#634—21no—
286#634C22×C412yes—
287C3×#67—24no—
288C3×#67—24no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—24no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C3×D12—21no—
296C3×D12C22×C412yes—
297C3×C4×D3C22×C412yes—
298C3×C4×D3C22×C412yes—
299C3×C4×D3C2×D412yes—
300C3×C4×D3C2×D412yes—
301C3×Dic6—21no—
302C3×Dic6C22×C412yes—
303#627—24no—
304#626—24no—
305#625—24no—
306#624—42no—
307#624C22⋊C414yes—
308D3×Dic3—24no—
309D3×Dic3—24no—
310D3×Dic3—24no—
311D3×Dic3C22⋊C414yes—
312D3×Dic3C22⋊C414yes—
313C32×C8—21no—
314C3⋊(C3⋊C8)—21no—
315C3×C3⋊C8—21no—
316C3×C3⋊C8—21no—
317C22×#41—91no—
318C22×M16—91no—
319C2×#117—91no—
320#419—91no—
321#419—91no—
322#418—31no—
323#418—91no—
324#417—91no—
325#417—91no—
326#417—91no—
327#417—91no—
328#416—31no—
329#416—91no—
330#416—91no—
331#416—91no—
332C24×C3—61no—
333C23×D3—21no—
334C23×D3—31no—
335C23×D3—31no—
336C3×#41—34no—
337C3×#41—62no—
338C2×C3×Q8—31no—
339C2×C3×D4—21no—
340C2×C3×D4—34no—
341C2×C3×D4—31no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—61no—
353C2×#67—68no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—121no—
359C22×Dic3—21no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—61no—
363C22×Dic3—68no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—121no—
369#239—34no—
370#239—62no—
371D3×Q8—34no—
372D3×Q8—62no—
373#237—22no—
374#237—34no—
375#237—34no—
376#237—34no—
377#237—34no—
378#237—64no—
379#237—62no—
380#237—68no—
381#237—68no—
382#237—62no—
383#237—62no—
384#237—68no—
385#237—62no—
386#237—122no—
387#237C4×D314yescomplemented
388D3×D4—22no—
389D3×D4—68no—
390D3×D4C4×D314yescomplemented
391#235—34no—
392#235—68no—
393#235—62no—
394C2×D12—61no—
395C2×D12C22×D311yescharacteristic
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—34no—
403C2×C4×D3—34no—
404C2×C4×D3—34no—
405C2×C4×D3—34no—
406C2×C4×D3—61no—
407C2×C4×D3—68no—
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×C4×D3—61no—
411C2×C4×D3—61no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3—121no—
416C2×C4×D3C22×D311yescharacteristic
417C2×C4×D3C22×D311yescharacteristic
418C2×Dic6—31no—
419C2×Dic6—31no—
420C2×Dic6—34no—
421C2×Dic6—61no—
422C2×Dic6—62no—
423C2×Dic6—61no—
424C2×Dic6—61no—
425C2×Dic6C22×D311yescharacteristic
426C3×M16—62no—
427C2×C3×C8—21no—
428C2×C3×C8—31no—
429C2×C3×C8—31no—
430C2×C3×C8—62no—
431C2×C3×C8C22×D311yescharacteristic
432C2×C3×C8C22×D311yescharacteristic
433C3×C4⋊C4—21no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4C22×D311yescharacteristic
437C3×C4⋊C4C22×D311yescharacteristic
438C3×C22⋊C4—61no—
439C3×C22⋊C4—61no—
440C3×C42—61no—
441C3×C42—61no—
442#217—61no—
443#217—61no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—61no—
448C4⋊Dic3—31no—
449C4⋊Dic3—31no—
450C4⋊Dic3—61no—
451C4⋊Dic3C22×D311yescharacteristic
452C4⋊Dic3C22×D311yescharacteristic
453Dic3⋊C4—61no—
454Dic3⋊C4—61no—
455Dic3⋊C4—61no—
456Dic3⋊C4—61no—
457Dic3⋊C4—121no—
458C4×Dic3—21no—
459C4×Dic3—21no—
460C4×Dic3—61no—
461C4×Dic3—61no—
462C4×Dic3—61no—
463C4×Dic3—61no—
464#208—62no—
465C2×C3⋊C8—31no—
466C2×C3⋊C8—31no—
467C2×C3⋊C8—61no—
468C2×C3⋊C8—62no—
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471ΓL(1,𝔽25)—22no—
472ΓL(1,𝔽25)—62no—
473ΓL(1,𝔽25)—62no—
474ΓL(1,𝔽25)—62no—
475ΓL(1,𝔽25)—62no—
476ΓL(1,𝔽25)—62no—
477ΓL(1,𝔽25)—122no—
478D3×C8—22no—
479D3×C8—62no—
480C22×C32—22no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32C22×D411yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3C2×C22⋊C412yes—
487C2×C3×D3—21no—
488C2×C3×D3—21no—
489C2×C3×D3—21no—
490C2×C3×D3—21no—
491C2×C3×D3—22no—
492C2×C3×D3—48no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3C2×C22⋊C412yes—
496C2×C3×D3C2×C22⋊C412yes—
497D32—44no—
498C32×C4—41no—
499C32×C4C23×C411yescharacteristic
500C32×C4C22×D411yescharacteristic
501C3⋊Dic3—22no—
502C3⋊Dic3—41no—
503C3⋊Dic3C2×C22⋊C412yes—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3C2×C22⋊C412yes—
508C3×Dic3C2×C22⋊C412yes—
509C2×#41—31no—
510C2×#41—91no—
511C2×#41—91no—
512C2×#41—98no—
513C2×#41—91no—
514C2×#41—181no—
515C2×#41—181no—
516C2×#41—184no—
517C22×Q8—91no—
518C22×D4—31no—
519C22×D4—181no—
520C23×C4—91no—
521C23×C4—181no—
522C2×M16—31no—
523C2×M16—91no—
524C2×M16—91no—
525C2×M16—91no—
526C2×M16—184no—
527C22×C8—31no—
528C22×C8—91no—
529#117—31no—
530#117—31no—
531#117—91no—
532#117—91no—
533#117—181no—
534#117—181no—
535C2×C4⋊C4—91no—
536C2×C4⋊C4—91no—
537C2×C22⋊C4—181no—
538C2×C42—181no—
539#103—31no—
540#103—31no—
541#103—91no—
542#103—91no—
543#103—91no—
544#103—91no—
545#103—91no—
546#103—91no—
547#102—31no—
548#102—31no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102D3211yescharacteristic, complemented
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—31no—
558C23×C3—31no—
559C23×C3—41no—
560C23×C3—64no—
561C23×C3—61no—
562C23×C3—122no—
563C23×C3—122no—
564C22×D3—21no—
565C22×D3—24no—
566C22×D3—31no—
567C22×D3—31no—
568C22×D3—34no—
569C22×D3—34no—
570C22×D3—42no—
571C22×D3—42no—
572C22×D3—61no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3D3×D411yescharacteristic
578C22×D3D3×D411yescharacteristic
579C3×Q8—32no—
580C3×Q8—61no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—22no—
584C3×D4—32no—
585C3×D4—41no—
586C3×D4—64no—
587C3×D4—64no—
588C3×D4—61no—
589C3×D4C2×C4×D312yes—
590C3×D4C2×C4×D312yes—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—41no—
601C2×C3×C4—64no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4C23×D311yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607#67—24no—
608#67—24no—
609#67—64no—
610#67—64no—
611#67—64no—
612#67—64no—
613#67—64no—
614#67—124no—
615C2×Dic3—21no—
616C2×Dic3—24no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—34no—
622C2×Dic3—34no—
623C2×Dic3—61no—
624C2×Dic3—64no—
625C2×Dic3—64no—
626C2×Dic3—64no—
627C2×Dic3—64no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—64no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—124no—
634C2×Dic3—121no—
635C2×Dic3—121no—
636C2×Dic3D3×D411yescharacteristic
637C2×Dic3D3×D411yescharacteristic
638D12—21no—
639D12—64no—
640D12C2×C4×D312yes—
641C4×D3—34no—
642C4×D3—34no—
643C4×D3—32no—
644C4×D3—32no—
645C4×D3—32no—
646C4×D3—32no—
647C4×D3—34no—
648C4×D3—34no—
649C4×D3—62no—
650C4×D3—62no—
651C4×D3—64no—
652C4×D3—64no—
653C4×D3—64no—
654C4×D3—122no—
655C4×D3—122no—
656C4×D3—122no—
657C4×D3—122no—
658C4×D3—242no—
659C4×D3C2×C4×D312yes—
660C4×D3C2×C4×D312yes—
661C4×D3D3×D412yes—
662C4×D3D3×D412yes—
663Dic6—21no—
664Dic6—32no—
665Dic6—32no—
666Dic6—62no—
667Dic6—64no—
668Dic6—61no—
669Dic6—61no—
670Dic6—64no—
671Dic6—121no—
672Dic6C2×C4×D312yes—
673C3×C8—21no—
674C3×C8—21no—
675C3×C8—41no—
676C3×C8—61no—
677C3×C8—61no—
678C3⋊C8—21no—
679C3⋊C8—21no—
680C3⋊C8—61no—
681C3⋊C8—61no—
682C3⋊C8—121no—
683C2×C32—42no—
684C2×C32C22×C22⋊C411yescharacteristic
685C2×C32#57511yescharacteristic
686C2×C32#57511yescharacteristic
687C3⋊D3—22no—
688C3×D3—22no—
689C3×D3—22no—
690C3×D3—42no—
691C24—61no—
692C24—91no—
693#41—34no—
694#41—62no—
695#41—94no—
696#41—94no—
697#41—94no—
698#41—182no—
699#41—188no—
700#41—182no—
701#41—188no—
702#41—182no—
703C2×Q8—31no—
704C2×Q8—94no—
705C2×Q8—91no—
706C2×Q8—181no—
707C2×Q8—182no—
708C2×D4—34no—
709C2×D4—31no—
710C2×D4—62no—
711C2×D4—61no—
712C2×D4—61no—
713C2×D4—181no—
714C2×D4—188no—
715C2×D4—181no—
716C2×D4—181no—
717C2×D4C2×D3211yescharacteristic
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—61no—
721C22×C4—91no—
722C22×C4—94no—
723C22×C4—94no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—91no—
727C22×C4—181no—
728C22×C4—181no—
729C22×C4—181no—
730C22×C4—188no—
731C22×C4—181no—
732C22×C4—181no—
733C22×C4—181no—
734M16—62no—
735M16—182no—
736M16—182no—
737M16—182no—
738C2×C8—31no—
739C2×C8—31no—
740C2×C8—62no—
741C2×C8—91no—
742C2×C8—182no—
743C2×C8C2×D3211yescharacteristic
744C4⋊C4—31no—
745C4⋊C4—31no—
746C4⋊C4—91no—
747C4⋊C4—181no—
748C4⋊C4—181no—
749C4⋊C4C2×D3211yescharacteristic
750C22⋊C4—61no—
751C22⋊C4—61no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C42—61no—
755C42—61no—
756C42—181no—
757C42—181no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—21no—
761C22×C3—32no—
762C22×C3—32no—
763C22×C3—42no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—61no—
769C22×C3—61no—
770C22×C3—61no—
771C22×C3—61no—
772C22×C3—62no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3—128no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×D3×D411yescharacteristic
780C2×D3—21no—
781C2×D3—21no—
782C2×D3—21no—
783C2×D3—21no—
784C2×D3—22no—
785C2×D3—32no—
786C2×D3—32no—
787C2×D3—48no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—62no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—124no—
798C2×D3—124no—
799C2×D3D3×C22⋊C412yes—
800C2×D3D3×C22⋊C412yes—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—32no—
804C3×C4—32no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—62no—
808C3×C4—81no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4C22×C4×D311yescharacteristic
812C3×C4C22×C4×D311yescharacteristic
813C3×C4C2×D3×D411yescharacteristic
814C3×C4C2×D3×D411yescharacteristic
815Dic3—22no—
816Dic3—32no—
817Dic3—32no—
818Dic3—41no—
819Dic3—41no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—122no—
824Dic3—121no—
825Dic3—121no—
826Dic3—241no—
827Dic3D3×C22⋊C412yes—
828Dic3D3×C22⋊C412yes—
829C32#289611yescharacteristic, complemented, Sylow
830C23—21no—
831C23—31no—
832C23—31no—
833C23—64no—
834C23—61no—
835C23—94no—
836C23—91no—
837C23—122no—
838C23—122no—
839C23—361no—
840C23—361no—
841Q8—32no—
842Q8—61no—
843Q8—92no—
844Q8—184no—
845Q8—181no—
846D4—21no—
847D4—32no—
848D4—64no—
849D4—64no—
850D4—61no—
851D4—184no—
852D4—184no—
853D4—184no—
854D4C4×D3212yes—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—64no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—94no—
867C2×C4—94no—
868C2×C4—94no—
869C2×C4—91no—
870C2×C4—92no—
871C2×C4—92no—
872C2×C4—184no—
873C2×C4—184no—
874C2×C4—184no—
875C2×C4—184no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—362no—
879C2×C4—362no—
880C2×C4C22×D3211yescharacteristic
881C8—21no—
882C8—61no—
883C8—61no—
884C8—181no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—42no—
889C2×C3—42no—
890C2×C3—62no—
891C2×C3—62no—
892C2×C3—82no—
893C2×C3—122no—
894C2×C3C2×D3×C22⋊C411yescharacteristic
895C2×C3C2×D3×C22⋊C411yescharacteristic
896C2×C3#576811yescharacteristic
897C2×C3#576811yescharacteristic
898C2×C3#577311yescharacteristic
899C2×C3#577311yescharacteristic
900D3—22no—
901D3—22no—
902D3—42no—
903D3—62no—
904D3—62no—
905D3—122no—
906C22—22no—
907C22—32no—
908C22—32no—
909C22—41no—
910C22—41no—
911C22—61no—
912C22—61no—
913C22—61no—
914C22—61no—
915C22—62no—
916C22—92no—
917C22—128no—
918C22—121no—
919C22—121no—
920C22—181no—
921C22—181no—
922C22—364no—
923C22D32×D411yescharacteristic
924C4—32no—
925C4—32no—
926C4—41no—
927C4—62no—
928C4—92no—
929C4—121no—
930C4—121no—
931C4—182no—
932C4—361no—
933C4C2×C4×D3211yescharacteristic
934C4D32×D411yescharacteristic
935C3—21no—
936C3#7883011yescharacteristic, complemented
937C3#7892411yescharacteristic, complemented
938C2—42no—
939C2—62no—
940C2—62no—
941C2—122no—
942C2—182no—
943C2D32×C22⋊C411yescharacteristic
944C2#1059472911yescharacteristic
945C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D3×ΓL(1,𝔽25)C2semidirect
3. #10594602C2semidirect
4. #10592470C2semidirect
5. C3×#4772C2semidirect
6. C3×#4770C2semidirect
7. #10591421C2semidirect
8. #10591420C2semidirect
9. #10591418C2semidirect
10. #10590957C2semidirect
11. #10590954C2semidirect
12. #10590948C2semidirect
13. #10590612C2semidirect
14. #10590608C2semidirect
15. #10590600C2semidirect
26. D3×#237C4semidirect
31. C2×#3743C22semidirect
32. C4⋊C4×C3⋊D3C22semidirect
34. C2×C3×D3×C8C22semidirect
36. C3×#892C22semidirect
38. #63900C22semidirect
43. #63841C22semidirect
44. C2×#3712C22semidirect
46. C2×D3×C3⋊C8C22semidirect
48. C32×#102C22semidirect
49. #63659C22semidirect
50. #63643C22semidirect
51. #63637C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. #63567C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63563C22semidirect
63. #63562C22semidirect
85. #4772D3semidirect
94. #4770D3semidirect
109. C3×#237C2×C4semidirect
111. C3×D3×D4C2×C4semidirect
135. #3795C2×C4semidirect
137. D3×Dic6C2×C4semidirect
208. C2×D3×C8C2×D3semidirect
212. #892C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
242. #832C2×D3semidirect
243. #832C2×D3semidirect
245. #821C2×D3semidirect
252. #816C2×D3semidirect
259. #810C2×D3semidirect
261. #809C2×D3semidirect
387. #237C4×D3semidirect
390. D3×D4C4×D3semidirect
554. #102D32semidirect
829. C32#2896semidirect
936. C3#78830semidirect
937. C3#78924semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D3×#2372
C2×D3×ΓL(1,𝔽25)2
#105946022
#105924702
C3×#47722
C3×#47702
#105914212
#105914202
#105914182
#105909572
#105909542
#105909482
#105906122
#105906082
#105906002
#789243
#788303